정상시계열과 random walk 자료생성

# A time series which contains no unit-root:
x = rnorm(1000)

# A time series which contains a unit-root:
y = cumsum(c(0, x))
par(mfrow=c(2,1))
plot.ts(x)
plot.ts(y)

단위근 검정 / 1차 차분 후 단위근 검정

adfTest(x)

## 
## Title:
##  Augmented Dickey-Fuller Test
## 
## Test Results:
##   PARAMETER:
##     Lag Order: 1
##   STATISTIC:
##     Dickey-Fuller: -22.6036
##   P VALUE:
##     0.01 
## 
## Description:
##  Mon Jun 22 00:48:53 2020 by user: jay

adfTest(y)

## 
## Title:
##  Augmented Dickey-Fuller Test
## 
## Test Results:
##   PARAMETER:
##     Lag Order: 1
##   STATISTIC:
##     Dickey-Fuller: -0.8042
##   P VALUE:
##     0.36 
## 
## Description:
##  Mon Jun 22 00:48:53 2020 by user: jay

#1차 차분 후 
adfTest(diff(y)) 

## 
## Title:
##  Augmented Dickey-Fuller Test
## 
## Test Results:
##   PARAMETER:
##     Lag Order: 1
##   STATISTIC:
##     Dickey-Fuller: -22.6036
##   P VALUE:
##     0.01 
## 
## Description:
##  Mon Jun 22 00:48:53 2020 by user: jay

plot.ts(diff(y))

PP Test

PP.test(x)

## 
##  Phillips-Perron Unit Root Test
## 
## data:  x
## Dickey-Fuller = -30.399, Truncation lag parameter = 7, p-value = 0.01

PP.test(y)

## 
##  Phillips-Perron Unit Root Test
## 
## data:  y
## Dickey-Fuller = -2.6131, Truncation lag parameter = 7, p-value = 0.3188

5장의 stock data를 이용하여 복습

data<-read.table("https://raw.githubusercontent.com/jaesanglee95/Jay_blog/master/stock.csv")
stock<-ts(data)
#stock data
plot.ts(stock)

adfTest(stock)

## 
## Title:
##  Augmented Dickey-Fuller Test
## 
## Test Results:
##   PARAMETER:
##     Lag Order: 1
##   STATISTIC:
##     Dickey-Fuller: 1.373
##   P VALUE:
##     0.9561 
## 
## Description:
##  Mon Jun 22 00:48:54 2020 by user: jay

PP.test(stock)

## 
##  Phillips-Perron Unit Root Test
## 
## data:  stock
## Dickey-Fuller = -1.1877, Truncation lag parameter = 4, p-value = 0.9064

로그변환 후 결과 확인

logstock<-log(stock)
plot(logstock)

adfTest(logstock)

## 
## Title:
##  Augmented Dickey-Fuller Test
## 
## Test Results:
##   PARAMETER:
##     Lag Order: 1
##   STATISTIC:
##     Dickey-Fuller: 2.6555
##   P VALUE:
##     0.99 
## 
## Description:
##  Mon Jun 22 00:48:54 2020 by user: jay

PP.test(logstock)

## 
##  Phillips-Perron Unit Root Test
## 
## data:  logstock
## Dickey-Fuller = -1.1894, Truncation lag parameter = 4, p-value = 0.9061

로그변환 후 1차 차분 후 결과 확인

diff_logstock<-diff(logstock, lag=1)
plot(diff_logstock)

adfTest(diff_logstock)

## 
## Title:
##  Augmented Dickey-Fuller Test
## 
## Test Results:
##   PARAMETER:
##     Lag Order: 1
##   STATISTIC:
##     Dickey-Fuller: -8.6082
##   P VALUE:
##     0.01 
## 
## Description:
##  Mon Jun 22 00:48:54 2020 by user: jay

PP.test(diff_logstock)

## 
##  Phillips-Perron Unit Root Test
## 
## data:  diff_logstock
## Dickey-Fuller = -13.318, Truncation lag parameter = 4, p-value = 0.01

KPSS test

앞선 두 가지 검정 방법과 가설이 반대이다.
귀무가설: 정상이다 vs 대립가설: random walk

kpss.test(diff_logstock)

## 
##  KPSS Test for Level Stationarity
## 
## data:  diff_logstock
## KPSS Level = 0.1983, Truncation lag parameter = 4, p-value = 0.1